Okay, first of all: purebreeding in dogs is not a bad thing. You look at a breed like golden retrievers, who are typically bred very pure, and they are as close as possible to free of any hereditary illnesses, with few genetic disorders and even a significantly lower risk of cancer than other dogs.
Also, the Kennel Club isn't trying to establish one breed of dog as superior. They just want variety. And for people who still use dogs for work (which I'm sure PETA doesn't take into account), purebreeding means that certain inherited traits--the herding instincts of sheepdogs, digging and tracking instincts of beagles or bloodhounds, etc--are not diluted by mixed heritage. Which matters, PETA loonies--and if you're ever kidnapped, I hope you won't complain when police use purebred bloodhounds to find you.
The really shocking thing about this is, of course, that PETA sees it as perfectly logical to compare purebreeding dogs to murdering Jews and blacks. Never mind that these dogs are not killed, are not even mistreated. The only thing purebreeding means is that they are kept away from dogs of different breeds while in heat. Oh, the horror! It's practically the same as slavery!
Well, no. Dogs are not people. And while it may be abominable to mistreat them, purebreeding is not really mistreatment. And even if it were, it's not equivalent to the Holocaust. Every decent human being should be mortally offended by this.